I am currently studying Computer Graphics, in which we made a graphics engine. While studying I came across something confusing regarding transformations. Rotations to be specific. In our course notes we are given how to get to the base transformations. These look like:
$$ R_x(\phi)= \left[ {\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & \cos(\phi) & -\sin(\phi) & 0 \\ 0 & \sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
$$ R_y(\phi)= \left[ {\begin{array}{cccc} \cos(\phi) & 0 & \sin(\phi) & 0 \\ 0 & 1 & 0 & 0 \\ -\sin(\phi) & 0 & \cos(\phi) & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
$$ R_z(\phi)= \left[ {\begin{array}{cccc} \cos(\phi) & -\sin(\phi) & 0 & 0 \\ \sin(\phi) & \cos(\phi) & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
However, these are not identical to the rotation formula's we had to use in our engines. The ones we had to use were
$$ R_x(\phi)= \left[ {\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & \cos(\phi) & \sin(\phi) & 0 \\ 0 & -\sin(\phi) & \cos(\phi) & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
$$ R_y(\phi)= \left[ {\begin{array}{cccc} \cos(\phi) & 0 & -\sin(\phi) & 0 \\ 0 & 1 & 0 & 0 \\ \sin(\phi) & 0 & \cos(\phi) & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
$$ R_z(\phi)= \left[ {\begin{array}{cccc} \cos(\phi) & \sin(\phi) & 0 & 0 \\ -\sin(\phi) & \cos(\phi) & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array} } \right] $$
Basically the sinus values all have the opposite sign. The given reason for this is: "In the course notes, base transformations are described. For our practicum we'll need point transformations. Therefore, use these and not the ones in the course notes."
I don't see why this is the case, what are the base transformations used for then? Why is only the sinus value affected by this?